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Exponents - Power Law - Variable Exponent Base with Known Power to Prime Base with Unknown Power (Level 1)

This math topic focuses on solving for unknown exponents using the Power Law. The problems involve rewriting expressions of exponentiated variables raised to particular powers and equating them to the same bases with unknown exponents. Students are tasked with finding these unknown exponents through simplification and application of exponent rules, specifically involving powers raised to other powers (i.e., \((b^n)^m = b^{n \cdot m}\)), and expressing the results in reduced form. Multiple choices for the correct exponent expressions are provided for each question. This set of problems is an introductory exercise in manipulating and understanding powers in algebraic contexts.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Power Law - Variable Exponent Base with Known Power to Prime Base with Unknown Power

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Solve for the missing exponent (?) in reduced form

(2n)2=2?(2^{n})^{2} = 2^{?}

Exponents - Power Law - Variable Exponent Base with Known Power to Prime Base with Unknown Power Worksheet

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Math worksheet on 'Exponents - Power Law - Variable Exponent Base with Known Power to Prime Base with Unknown Power (Level 1)'. Part of a broader unit on 'Exponents - Multiplication and Division - Advanced' Learn online: app.mobius.academy/math/units/exponents_multiplication_and_division_advanced/
1
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 3 = 2 to the power of ?
a A LaTex expression showing ?=15n over 1
b A LaTex expression showing ?=3n over 5
c A LaTex expression showing ?=3 over 5n
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=2 over n
f A LaTex expression showing ?=3n
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (2 to the power of n ) to the power of 2 = 2 to the power of ?
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=6n over 1
c A LaTex expression showing ?=3n over 6
d A LaTex expression showing ?=2 over 3n
e A LaTex expression showing ?=3 over 6n
f A LaTex expression showing ?=2n
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 3 = 3 to the power of ?
a A LaTex expression showing ?=3n over 9
b A LaTex expression showing ?=9n over 1
c A LaTex expression showing ?=3n
d A LaTex expression showing ?=3 over 9n
e A LaTex expression showing ?=3n over 3
f A LaTex expression showing ?=3 over 3n
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (4 to the power of n ) to the power of 3 = 4 to the power of ?
a A LaTex expression showing ?=3n over 2
b A LaTex expression showing ?=n
c A LaTex expression showing ?=6n
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=6n over 1
f A LaTex expression showing ?=3n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (6 to the power of n ) to the power of 2 = 6 to the power of ?
a A LaTex expression showing ?=2 over 2n
b A LaTex expression showing ?=6n over 1
c A LaTex expression showing ?=8n
d A LaTex expression showing ?=2n
e A LaTex expression showing ?=2 over 4n
f A LaTex expression showing ?=6 over n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (4 to the power of n ) to the power of 2 = 4 to the power of ?
a A LaTex expression showing ?=2n over 3
b A LaTex expression showing ?=3 over 6n
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=3n
e A LaTex expression showing ?=3n over 6
f A LaTex expression showing ?=4n over 1
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing (3 to the power of n ) to the power of 2 = 3 to the power of ?
a A LaTex expression showing ?=3n
b A LaTex expression showing ?=2 over 4n
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=2n over 4
e A LaTex expression showing ?=3n over 1
f A LaTex expression showing ?=n